2) A bullet of mass m1 = 0.01 kg and velocity v = 100 m/s is fired into a 100 kg block of ice and gets stuck. How fast does the ice move after the bullet impacts it?
To find the speed at which the ice moves after the bullet impacts it, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. So before the collision, the momentum of the bullet is given by the equation:
Momentum of bullet = mass of bullet * velocity of bullet
Since the bullet gets stuck in the ice, the total mass after the collision is the sum of the mass of the bullet and the mass of the ice. Therefore:
Total mass after collision = mass of bullet + mass of ice
To find the velocity at which the ice moves after the collision, we can rearrange the equation for the conservation of momentum:
momentum before collision = momentum after collision
mass of bullet * velocity of bullet = total mass after collision * velocity after collision
Substituting the given values into the equation:
0.01 kg * 100 m/s = (0.01 kg + 100 kg) * velocity after collision
Simplifying the equation:
1 kg * m/s = 100.01 kg * velocity after collision
Now, we can solve for the velocity after the collision:
velocity after collision = (0.01 kg * 100 m/s) / 100.01 kg
velocity after collision ≈ 0.01 m/s
Therefore, the ice moves at a speed of approximately 0.01 m/s after the bullet impacts it.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity (p = m * v).
Let's denote the initial velocity of the ice as v2 and the final velocity of the ice-bullet system as vf.
Before the collision, the bullet's momentum is given by p1 = m1 * v. The ice block is initially at rest, so its momentum is given by p2 = m2 * 0 (where m2 is the mass of the ice block).
The total initial momentum is then p_initial = p1 + p2 = m1 * v.
After the collision, the bullet is stuck in the ice block, and they move together with a final velocity vf. The total momentum after the collision is given by p_final = (m1 + m2) * vf.
Applying the principle of conservation of momentum, we have:
p_initial = p_final
m1 * v = (m1 + m2) * vf
0.01 kg * 100 m/s = (0.01 kg + 100 kg) * vf
1 kg * m/s = 100.01 kg * vf
vf = (1 kg * m/s) / (100.01 kg)
vf ≈ 0.009995 m/s
Therefore, the final velocity of the ice-bullet system after the bullet impacts it is approximately 0.009995 m/s.